Question

problem 5 write an inequality in terms of x that represents the graph. -10 -8 -6 -4 -2 0 2 4 6 8 10

Explanation:

Step1: Analyze the number line graph

The number line has a closed dot at -5? Wait, no, looking at the graph, the closed dot is at -5? Wait, the marks: -10, -8, -6, -4? Wait, no, the labels: -10, -8, -6, then a dot at -5? Wait, no, the x - axis: the tick marks are at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. The closed dot is at -5? Wait, no, between -6 and -4, the dot is at -5? Wait, no, the position: the dot is at -5? Wait, no, the graph shows a closed dot at -5? Wait, no, let's check again. The number line: the tick marks are -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. The closed dot is at -5? Wait, no, the dot is at -5? Wait, no, the purple line starts at a closed dot and goes to the right. Wait, the closed dot is at -5? Wait, no, the x - coordinate of the closed dot: between -6 and -4, the middle is -5? Wait, no, the tick marks are at -10, -8, -6, -4, so the dot is at -5? Wait, no, maybe I misread. Wait, the labels: -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. So the closed dot is at -5? Wait, no, the dot is at -5? Wait, no, the graph: the closed dot is at -5? Wait, no, let's see the position. The arrow is to the right, so the inequality is x is greater than or equal to the value of the closed dot. Wait, the closed dot is at -5? Wait, no, maybe the dot is at -5? Wait, no, the tick marks: -10, -8, -6, -4, so the distance between -6 and -4 is 2 units, so the midpoint is -5. So the closed dot is at -5, and the line goes to the right. So the inequality is \(x\geq - 5\)? Wait, no, wait the original graph: let's check again. The user's graph: the number line has a closed dot at -5? Wait, no, the labels are -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. The closed dot is at -5? Wait, no, maybe the dot is at -5? Wait, no, perhaps I made a mistake. Wait, the graph shows a closed dot at -5 and the line extending to the right. So the inequality is \(x\geq - 5\)? Wait, no, wait the closed dot is at -5, so the solution set includes -5 and all numbers greater than -5. So the inequality is \(x\geq - 5\). Wait, but let's confirm. A closed dot means the value is included, and the arrow to the right means greater than or equal to. So if the closed dot is at -5, then \(x\geq - 5\).

Wait, maybe the dot is at -5? Wait, no, the tick marks: -10, -8, -6, -4, so the dot is at -5? Wait, no, the distance between -6 and -4 is 2, so the dot is at -5. So the inequality is \(x\geq - 5\).

Step2: Formulate the inequality

Since the closed dot is at \(x = - 5\) and the line is shaded to the right, the inequality is \(x\) is greater than or equal to \(-5\), which is written as \(x\geq - 5\).

Answer:

\(x\geq - 5\)